Q9 of 176 Page 20

The common ratio of a G.P. is 3, and the last term is 486. If the sum of these terms be 728, find the first term.

Given: Common Ratio = 3


Sum of GP = 728


Sum of GP for n terms =


Last term say it be n


∴ Tn = arn - 1


⇒ 486 = a3n - 1


⇒


⇒ 1458 = a.3n …(1)


⇒


⇒


⇒ 1456 = a.3n - a…(2)


Subtracting 1 from 2 we get


⇒ 1458 - 1456 = a.3n - a.3n + a


⇒ a = 2.


∴ The first term is 2.


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